Such a sky would be roughly as bright as 150,000 suns like ours, and do you question that under those conditions life on Earth would be impossible?
However, the sky is not as bright as 150,000 suns. The night sky is black. Somewhere in the Olbers' paradox there is some mitigating circumstance or some logical error..
Olbers himself thought he found it. He suggested that space was not truly transparent; that it contained clouds of dust and gas which absorbed most of the starlight, allowing only an insignificant fraction to reach the Earth.
That sounds good, but it is no good at all. There are indeed dust clouds in space but if they absorbed all the starlight that fell upon them (by the reasoning of Olbers' paradox) then their temperature would go up until they grew hot enough to be luminous. They would, eventually, emit as much light as they absorb and the Earth sky would still be star-bright over all its extent.
But if the logic of an argument is faultless and the con clusion is still wrong, we must investigate the assumptions.
What about Assumption 2, for instance? Are the stars in deed infinite in number and evenly spread throughout the universe?
Even in Olbers' time there seemed reason to believe this assumption to be false. The German-English astronomer William Herschel made counts of stars of different bright ness. He assumed that, on the average, the dimmer stars were more distant than the bright ones (which follows from Assumption 3) and found that the density of the stars in space fell off with distance.
From the rate of decrease in density in different direc tions, Herschel decided that the stars made up a lens shaped figure. The long diameter, he decided, was 150 times the distance from the Sun to Arcturus (or 6000 light-years, we would now say), and the whole conglomer ation would consist of 100,000,000 stars.
This seemed to dispose of Olbers' paradox. If the lens shaped conglomerate (now called the Galaxy) truly con tained all the stars in existence, then Assumption 2 breaks down. Even if we imagined space to be infinite in extent outside the Galaxy (Assumption 1), it would contain no stars and would contribute no illumination. Consequently, there would be only a finite number of star-containing shells and only a finite (and not very large) amount of illumination would be received on Earth. That would be why the night sky is black.
The estimated size of the Galaxy has been increased since Herschel's day. It is now believed to be 100,000 light-years in diameter, not 6000; and to contain 150,000, 000,000 stars, not 100,000,000. This change, however, is not crucial; it still leaves the night sky black.
In the twentieth century Olbers' paradox came back to life, for it came to be appreciated that there were indeed stars outside the Galaxy.
The foggy patch in Andromeda had been felt through out the nineteenth century to be a luminous mist that formed part of our own Galaxy. However, other such patches of mist (the Orion Nebula, for instance) contained stars that lit up the mist. The Andromeda patch, on the other hand, seemed to contain no stars but to glow of itself.
Some astronomers began to suspect the truth, but it wasn't definitely established until 1924, when the Amer ican astronomer Edwin Powell Hubble turt'ied the 100 inch telescope on the glowing mist and was able to make out separate stars in its outskirts. These stars were in dividually so dim that it became clear at once that the patch must be hundreds of thousands of light-years away from us and far outside the Galaxy. Furthermore, to be seen, as it was, at that distance, it must rival in size our entire Galaxy and be another galaxy in its own right.
And so it is. It is now believed to be over 2,000,000 light-years from us and to contain at least 200,000,000, 000 stars. Still other galaxies were discovered at vastly greater distances. Indeed, we now suspect that within the observable universe there are at least 100,000,000,000 galaxies, and the distance of some of them has been esti mated as high as 6,000,000,000 light-years.
Let us take Olbers' three assumptions then and substi tute the word "galaxies" for "stars" and see how they sound.
Assumption 1, that the universe is infinite, sounds good.
At least there is no sign of an end even out to distances of billions of light-years.
Assumption 2, that galaxies (not stars) are infinite in number and evenly spread throughout the universe, sounds good, too. At least they are evenly distributed for as far out as we can see, and we can see pretty far.
Assumption 3, that galaxies (not stars) are of uniform average brightness throughout space, is harder to handle.
However, we have no reason to suspect,-6at distant galaxies are consistently larger or smaller than nearby ones, and if the galaxies come to some uniform average size and star-content, then it certainly seems reasonable to suppose they are uniformly bright as well.
Well, then, why is the night sky black? We're back to that.
Let's try another tack. Astronomers can determine whether a distant luminous object is approaching us- or receding from us by studying its spectrum (that is, its lijzht as spread out in a rainbow of wavelengths from short wavelength violet to long-wavelength red).
The spectrum is crossed by dark lines which are in a fixed position if the object is motionless with respect to us. If the object is approaching us, the lines shift toward the violet. If the object is receding from us, the lines shift toward the red. From the size of the shift astronomers can determine the velocity of approach or recession.
In the 1910s and 1920s the spectra of some galaxies (or bodies later understood to be galaxies) were studied, and except for one or two of the very nearest, all are re ceding from us. In fact, it soon became apparent that the farther galaxies are receding more rapidly than the nearer ones. Hubble was able to formulate what is now called "Hubble's Law" in 1929. This states that the velocity of recession of a galaxy is proportional to its distance from us. If Galaxy A is twice as far as Ga laxy D, it is receding at twice the velocity. The farthest observed galaxy, 6,000, 000,000 light-years from us, is receding at a velocity half that of light.
The reason for Hubble's Law is taken to lie in the ex pansion of the universe itseff-an expansion which can be made to follow from the equations set up by Einstein's General Theory of Relativity (which, I hereby state firmly, I will not go into).
Given the expansion of the universe, now, how are Olbers' assumptions affected?
If, at a distance of 6,000,000,000 light-years a galaxy recedes at half the speed of light, then at a distance of 12,000,000,000 light-years a galaxy ought to be receding at the speed of light (if Hubble's Law holds). Surely, further distances are meaningless, for we cannot halve velocities greater than that of light. Even if that were pos sible, no light, or any other "message" could reach us from such a more-distant galaxy and it would not, in effect, be in our universe. Consequently, we can imagine the universe to be finite after all, with a "Hubble radius" of some 12,000,000,000 light-years.
But that doesn't wipe out Olbers' paradox. Under the requirements of Einstein's theories, as galaxies move faster and faster relative to an observer, they become shorter and shorter in the line of travel and take up less and less space, so that there is room for larger and larger numbers of galaxies. In fact, even in a finite universe, with a radius of 12,000,000,000 light-years, there might still be an in finite number of galaxies; almost all of them (paper-thin) existing in the outermost few miles of the Universe-sphere.
So Assumption 2 stands even if Assumption I does not; and Assumption 2, by itself, can be enough to insure a star-bright sky.
But what about the red shift?
Astronomers measure the red shift by the change in position of the spectral lines, but those lines move only because the entire spectrum moves. A shift to the red is a shift in the direction of lesser energy. A receding galaxy delivers less radiant energy to the Earth than the same galaxy would deliver if it were standing still relative to us - just because of the red shift. The faster a galaxy recedes the less radiant energy it delivers. A galaxy receding at the speed of light delivers no radiant energy at all no matter how bright it might be.